Question: Simplify the following expression: $r = \dfrac{t^2 - t - 2}{t - 2} $
First factor the polynomial in the numerator. $ t^2 - t - 2 = (t - 2)(t + 1) $ So we can rewrite the expression as: $r = \dfrac{(t - 2)(t + 1)}{t - 2} $ We can divide the numerator and denominator by $(t - 2)$ on condition that $t \neq 2$ Therefore $r = t + 1; t \neq 2$